Given:
To find:
We need to find the perimeter of DEFG.
Explanation:
The given quadrilateral DEFG is rhombus since it has four sides with equal length.
The endpoints of the DG are (1,2) and (5,3).
Consider the distance formula.
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\text{Substitute }x_1=1,x_2=5,y_1=2\text{ and, }y_2=3\text{ in the formula to find the length of DG.}[/tex][tex]DG=\sqrt[]{(5-1)^2+(3-2)^2}[/tex]
[tex]DG=\sqrt[]{4^2+1^2}[/tex]
[tex]DG=\sqrt[]{17^{}}[/tex]
The perimeter of the rhombus.
[tex]P=4a[/tex][tex]\text{Substitute DG=a=}\sqrt[]{17}\text{ in the formula.}[/tex]
[tex]P=4\sqrt[]{17}\text{ units.}[/tex]
Final answer:
[tex]Perimeter\text{ of DEFG =4}\sqrt[]{17\text{ units.}}[/tex]
